The s-6 designation is on a 1973 Schwinn I have, the tires even say to fit Schwinn s-6 rims on them. I don't think that particular s-6 rim is anywhere near the 1930's.
It is what Schwinn called a tubular rim in the 60's - 70's. Not for tubular tires, that's something different, the rim has a hollow tube in each side making it very strong. The dealers often had a short piece of a rim cut away to show customers. I know someone who was there in those days.
The trike in my sig is 1973 Schwinn it has three of them in 24".
I don't know much about old bikes, but the BSA in the chain ring was a company in England that made bicycles and motorcycles. -- Birmingham Small Arms.
I have ridden 650cc and a 500cc(?) BSA motorcycles. I think the motorcycles were from the 1960's or the early 1970's. They stopped making them.
Whatever your bike is it sure is nice.